T3 = 1+ 1/2+ 1/3 = 1 1/6t 1+T2 = 5/2 T3- 1 = 5/6g(3)= 3

Guess g(n)=n

Proof: 1) When n=2, it has been proved;

2) When n≥2, it is assumed that the equation holds when n=k, that is

T 1+T2+…+T(k- 1)=(Tk- 1)k

Then when n=k+ 1

T 1+T2+…+T(k- 1)+Tk =(Tk- 1)k+Tk =( 1+k)Tk-k

=( 1+k)(T(k+ 1)- 1/(k+ 1))-k

=( 1+k)T(k+ 1)-k- 1

=(T(k+ 1)- 1)(k+ 1)

This equation also holds.

To sum up (1)(2), we can get g (n) = n